How to get a lighthouse to shine a lightbeam
It looks like this node setup works not too bad:


I've created a simple light ball for the light source, maybe you should add a bit of glow around as it's explained here: How do I make a luminescent gas cloud?
Now, for the beam, first, create a conic cylinder.
For the length gradient, mix an Emission node with a Transparent node, use a Gradient as factor, and a ColorRamp to control its intensity.
For the width gradient, mix the first Mix Shader with the Transparent node, use a Layer Weight as factor, and a ColorRamp to control its intensity.
To add a bit of noise you could mix the previous nodes with the Transparent node, with a Noise texture as a factor.